Critical RSOS and Minimal Models II: Building Representations of the Virasoro Algebra and Fields

Details Critical RSOS and Minimal Models II: Building Representations of the Virasoro Algebra and Fields Critical RSOS and Minimal Models II: Building Representations of the Virasoro Algebra and Fields

2002-11-20

arxiv.org/abs/hep-th/0211186v1

Nucl.Phys.B663:409-442,2003

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1016/S0550-3213(03)00375-4

We consider sl(2) minimal conformal field theories and the dual parafermion models. Guided by results for the critical A_L Restricted Solid-on-Solid (RSOS) models and its Virasoro modules expressed in terms of paths, we propose a general level-by-level algorithm to build matrix representations of the Virasoro generators and chiral vertex operators (CVOs). We implement our scheme for the critical Ising, tricritical Ising, 3-state Potts and Yang-Lee theories on a cylinder and confirm that it is consistent with the known two-point functions for the CVOs and energy-momentum tensor. Our algorithm employs a distinguished basis which we call the L_1-basis. We relate the states of this canonical basis level-by-level to orthonormalized Virasoro states.

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